Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms

摘要

This paper is devoted to studying the null and approximate controllability oftwo linear coupled parabolic equations posed on a smooth domain of R^N (N>1)with coupling terms of zero and first orders and one control localized in somearbitrary nonempty open subset of the domain. We prove the null controllabilityunder a new sufficient condition and we also provide the first example of a notapproximately controllable system in the case where the support of one of thenontrivial first order coupling terms intersects the control domain.